This document discusses inventory management concepts. It defines inventory as stock of materials or stored capacity. The main types of inventory are raw materials, work in progress, maintenance/repair/operating supplies, and finished goods. Inventory has costs associated with it like holding, ordering, and setup costs. Methods to optimize inventory levels include the economic order quantity model, production order quantity model, and ABC analysis for inventory classification and control. The reorder point indicates when inventory levels fall to a level where a new order should be placed.

1. Operations
Management
Inventory Management
Chapter 9
9-1 OPM 533

2. What is Inventory?
 Stock of materials
 Stored capacity © 1995
Corel Corp.
 Examples
© 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co.
© 1995 Corel Corp.
9-2 OPM 533

3. The Functions of Inventory
 To ”decouple” or separate various parts of the
production process
 To provide a stock of goods that will provide a
“selection” for customers
 To take advantage of quantity discounts
 To hedge against inflation and upward price
changes
9-3 OPM 533

4. Types of Inventory
 Raw material (RM)
 Work-in-progress (WIP)
 Maintenance/repair/operating supply (MRO)
 Finished goods (FG)
9-4 OPM 533

5. Disadvantages of Inventory
 Higher costs
 Item cost (if purchased)
 Ordering (or setup) cost
 Costs of forms, clerks’ wages etc.
 Holding (or carrying) cost
 Building lease, insurance, taxes etc.
 Difficult to control
 Hides production problems
9-5 OPM 533

6. Inventory Classifications
Inventory © 1984-1994
T/Maker Co.
Process Number Deman
Other
stage & Value d Type
Raw Material A
Independen Maintenanc
WIP Items
t e Operating
Finished B
Dependent
Goods Items
9-6 OPM 533 C
Items

7. The Material Flow Cycle
Other Wait Move Queu Setup Run
Time Time e Time Time
Input Time Output
Cycle Time
1 Run time: Job is at machine and being worked on
2 Setup time: Job is at the work station, and the work station is
being "setup."
3 Queue time: Job is where it should be, but is not being
processed because other work precedes it.
4 Move time: The time a job spends in transit
5 Wait time: When one process is finished, but the job is
waiting to be moved to the next work area.
6 Other: "Just-in-case" inventory.
9-7 OPM 533

8. ABC Analysis
 Divides on-hand inventory into 3 classes
 A class, B class, C class
 Basis is usually annual $ volume
 $ volume = Annual demand x Unit cost
 Policies based on ABC analysis
 Develop class A suppliers more
 Give tighter physical control of A items
 Forecast A items more carefully
9-8 OPM 533

9. Classifying Items as ABC
% Annual $ Class % $ Vol % Items
Usage A 80 15
100
B 15 30
80
C 5 55
60
A
40
B
20 C
0
0 50 100
% of Inventory Items
9-9 OPM 533

10. Cycle Counting
 Physically counting a sample of total inventory on
a regular basis
 Used often with ABC classification
 A items counted most often (e.g., daily)
9-10 OPM 533

11. Advantages of Cycle Counting
 Eliminates shutdown and interruption of
production necessary for annual physical
inventories
 Eliminates annual inventory adjustments
 Provides trained personnel to audit the accuracy
of inventory
 Allows the cause of errors to be identified and
remedial action to be taken
 Maintains accurate inventory records
9-11 OPM 533

12. Techniques for Controlling Service
Inventory Include:
 Good personnel selection, training, and discipline
 Tight control of incoming shipments
 Effective control of all goods leaving the facility
9-12 OPM 533

13. Independent versus
Dependent Demand
 Independent demand - demand for item is
independent of demand for any other item
 Dependent demand - demand for item is
dependent upon the demand for some other item
9-13 OPM 533

14. Inventory Costs
 Holding costs - associated with holding or
“carrying” inventory over time; e.g. obsolescence,
insurance, extra staffing, interest, pilferage,
damage, warehousing, etc.
 Ordering costs - associated with costs of placing
order and receiving goods; eg. Supplies, forms,
order processing, clerical support, etc.
 Setup costs - cost to prepare a machine or
process for manufacturing an order; e.g. clean-up
costs, re-tooling costs, adjustment costs, etc.
9-14 OPM 533

15. Inventory Holding Costs
(Approximate Ranges)
Cost as a
Category % of Inventory Value
Housing costs (building rent, depreciation, 6%
operating cost, taxes, insurance) (3 - 10%)
Material handling costs (equipment, lease 3%
or depreciation, power, operating cost) (1 - 3.5%)
Labor cost from extra handling 3%
(3 - 5%)
Investment costs (borrowing costs, taxes, 11%
and insurance on inventory) (6 - 24%)
Pilferage, scrap, and obsolescence 3%
(2 - 5%)
26%
Overall carrying cost
9-15 OPM 533

16. Inventory Models
 Fixed order-quantity models
 Economic order quantity Help answer the
 Production order quantity
inventory
planning
 Quantity discount questions!
 Probabilistic models
 Fixed order-period models
© 1984-1994
T/Maker Co.
9-16 OPM 533

17. 1. EOQ Assumptions
 Known and constant demand
 Known and constant lead time
 Instantaneous receipt of material
 No quantity discounts
 Only order (setup) cost and holding cost
 No stockouts
9-17 OPM 533

18. Inventory Usage Over Time
Order quantity = Usage Rate
Q (maximum Average
inventory level) Inventory
(Q*/2)
Inventory Level
Minimum
inventory0
Time
9-18 OPM 533

19. EOQ Model
How Much to Order?
Annual Cost
tC urve
s
l Co urv
e
Tota tC
Minimu
g Cos
m total
Ho ldin
cost
Order (Setup) Cost Curve
Optimal Order quantity
Order Quantity (Q*)
9-19 OPM 533

20. Why Holding Costs Increase
 More units must be stored if more are ordered
Purchase Order
Purchase Order Description Qty.
Description Qty. Microwave 1000
Microwave 1
Order
Order quantity
quantity
9-20 OPM 533

21. Why Order Costs Decrease
Cost is spread over more units
Example: You need 1000 microwave ovens
1 Order (Postage $ 0.33) 1000 Orders (Postage $330)
Purchase Order PurchaseOrder
Order
PurchaseOrder
Description Purchase
Description Qty.
Purchase OrderQty.
Qty. Description Qty.
Microwave 1000 Description Qty. 1
Microwave
Description
Microwave 11
Microwave 1
Microwave
Order
quantity
9-21 OPM 533

22. Deriving an EOQ
1. Develop an expression for setup or ordering
costs
2. Develop an expression for holding cost
3. Set setup cost equal to holding cost
4. Solve the resulting equation for the best order
quantity
9-22 OPM 533

23. EOQ Model Equations
Optimal Order Quantity = Q* = 2 ×D ×S
H
D
Expected Number of Orders N =
=
Q*
Expected Time Between Orders = T = Working Days / Year
N
D D = Demand per year
d=
Working Days / Year S = Setup (order) cost per
order
ROP = d × L H = Holding (carrying) cost
d = Demand per day
L = Lead time in days
9-23 OPM 533

24. The Reorder Point (ROP) Curve
Q*
Slope = units/day = d
Inventory level
ROP
(Units)
(units)
Time
Lead time = L (days)
9-24 OPM 533

25. 2. Production Order Quantity Model
 Answers how much to order and when to order
 Allows partial receipt of material
 Other EOQ assumptions apply
 Suited for production environment
 Material produced, used immediately
 Provides production lot size
 Lower holding cost than EOQ model
9-25 OPM 533

26. Reasons for Variability in Production
Most variability is caused by waste or by poor
management. Specific causes include:
u employees, machines, and suppliers produce
units that do not conform to standards, are late or
are not the proper quantity
u inaccurate engineering drawings or specifications
u production personnel try to produce before
drawings or specifications are complete
u customer demands are unknown
9-26 OPM 533

27. POQ Model Equations
2*D*S
Optimal Order Quantity = Q* =
p
( )
d
H* 1 -
p
Maximum inventory level Q*
= ( )
1 -
d
p
D D = Demand per year
Setup Cost = * S
Q S = Setup cost
H = Holding cost
Holding Cost
( )
= 0.5 * H * Q 1 -
d
p
d = Demand per day
p = Production per
9-27 OPM 533 day

28. 3. Quantity Discount Model
 Answers how much to order &
when to order
 Allows quantity discounts
 Reduced price when item is purchased in larger
quantities
 Other EOQ assumptions apply
 Trade-off is between lower price & increased
holding cost
9-28 OPM 533

29. Inventory Usage Over Time
Usage rate Average
Order inventory
quantity = Q
Inventory level
on hand
(maximum
Q
inventory
level) 2
Minimum
inventory
Time
Figure 12.3
29

30. Minimizing Costs
Objective is to minimize total costs
Curve for total
cost of holding
and setup
Minimum
total cost
Annual cost
Holding cost
curve
Setup (or order)
cost curve
Optimal Order quantity
Table 11.5 order
30
quantity

31. The EOQ Model Annual setup cost =
D
Q
S
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the Inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual setup cost = (Number of orders placed per year)
x (Setup or order cost per order)
Annual demand Setup or order
=
Number of units in each order cost per order
D
= (S)
Q
31

32. The EOQ Model Annual setup cost =
D
Q
S
Q
Annual holding cost = H
Q = Number of pieces per order 2
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the Inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual holding cost = (Average inventory level)
x (Holding cost per unit per year)
Order quantity
= (Holding cost per unit per year)
2
Q
= ( H)
2
32

33. The EOQ Model Annual setup cost =
D
Q
S
Q
Annual holding cost = H
Q = Number of pieces per order 2
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the Inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup cost
equals annual holding cost
D Q
S = H
Q 2
Solving for Q*
2DS = Q2H
Q2 = 2DS/H
33
Q* = 2DS/H

34. An EOQ Example
Determine optimal number of needles to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
2DS
Q* =
H
2(1,000)(10)
Q* = = 40,000 = 200 units
0.50
34

35. An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order
H = $.50 per unit per year
Expected Demand D
number of = N = =
orders Order quantity Q*
1,000
N= = 5 orders per year
200
35

36. An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year
Number of working
Expected days per year
time between = T =
orders N
250
T= = 50 days between orders
5
36

37. An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost
D Q
TC = S + H
Q 2
1,000 200
TC = ($10) + ($.50)
200 2
TC = (5)($10) + (100)($.50) = $50 + $50 = $100
37

38. An EOQ Example with safety stock
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
Safety Stock (ss) = 10 units
Total annual cost = Setup cost + Holding cost
D Q
TC = S + ( + ss)H
Q 2
1,000 200
TC = ($10) + (100 + )($.50)
200 2
TC = (5)($10) + (200)($.50) = $50 + $100 = $150
38

39. Reorder Points
 EOQ answers the “how much” question
 The reorder point (ROP) tells when to
order
Demand Lead time for a
ROP = per day new order in days
=dxL
D
d = Number of working days in a year
39

40. Reorder Point Curve
Q*
Inventory level (units)
Slope = units/day = d
ROP
(units)
Time (days)
Figure 12.5 Lead time = L
40

41. Reorder Point Example
Demand = 8,000 DVDs per year
250 working day year
Lead time for orders is 3 working days
D
d=
Number of working days in a year
= 8,000/250 = 32 units
ROP = d x L
= 32 units per day x 3 days = 96 units
41

42. Reorder point with Safety Stock
Annual Demand = 25,000 units
Number of working days in a year 250 days
Lead time = 5 days
Safety stock (ss) = 2 days usage
ROP = d x l + ss
d= D / Number of days work in a year
d= 25,000 / 250 = 100 units
ss= 2 days x 100 = 200
ROP = 100 x 5 + 200 = 700 units
42

43. Quantity Discount Models
 Reduced prices are often available when
larger quantities are purchased
 Trade-off is between reduced product cost
and increased holding cost
Total cost = Setup cost + Holding cost + Product cost
D QH
TC = S+ + PD
Q 2
43

44. Quantity Discount Models
A typical quantity discount schedule
Discount Discount
Number Discount Quantity Discount (%) Price (P)
1 0 to 999 no discount $5.00
2 1,000 to 1,999 4 $4.80
3 2,000 and over 5 $4.75
Table 12.2
44

45. Quantity Discount Models
Steps in analyzing a quantity discount
1. For each discount, calculate Q*
2. If Q* for a discount doesn’t qualify,
choose the smallest possible order size
to get the discount
3. Compute the total cost for each Q* or
adjusted value from Step 2
4. Select the Q* that gives the lowest total
cost
45

46. Quantity Discount Models
Total cost curve for discount 2
Total cost
curve for
discount 1
Total cost $
Total cost curve for discount 3
b
a Q* for discount 2 is below the allowable range at point a
and must be adjusted upward to 1,000 units at point b
1st price 2nd price
break break
0 1,000 2,000
Figure 12.7
46 Order quantity

47. Quantity Discount Example
Calculate Q* for every discount 2DS
Q* =
IP
2(5,000)(49)
Q1* = = 700 cars order
(.2)(5.00)
2(5,000)(49)
Q2* = = 714 cars order
(.2)(4.80)
2(5,000)(49)
Q3* = = 718 cars order
(.2)(4.75)
47

48. Quantity Discount Example
Calculate Q* for every discount 2DS
Q* =
IP
2(5,000)(49)
Q1* = = 700 cars order
(.2)(5.00)
2(5,000)(49)
Q2* = = 714 cars order
(.2)(4.80) 1,000 — adjusted
2(5,000)(49)
Q3* = = 718 cars order
(.2)(4.75) 2,000 — adjusted
48

49. Quantity Discount Example
Annual Annual Annual
Discount Unit Order Product Ordering Holding
Number Price Quantity Cost Cost Cost Total
1 $5.00 700 $25,000 $350 $350 $25,700
2 $4.80 1,000 $24,000 $245 $480 $24,725
3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50
Table 12.3
Choose the price and quantity that gives
the lowest total cost
Buy 1,000 units at $4.80 per unit
49